Exact, numerical, and mean field behavior of a dimerizing lattice in one dimension

Abstract The thermodynamics and dynamics of a one-dimensional dimer-forming anharmonic model is studied in the classical limit. This model mimics the behavior of materials with a Peierls instability. Specific heat C ( T ), correlation length l c ( T ), and order parameter are calculated in three ways: (a) by mean-field (MF) approximation, (b) by numerical molecular dynamics (MD) simulation, and (c) by an exact transfer matrix method. The neighbor distribution function F ( x ) and vibrational density-of-states D ( ω ) (Fourier transform of velocity–velocity correlation function) are found numerically. MF theory fails completely to describe the destruction of long-range order by fluctuations, but nevertheless, the MF answers for C ( T ), l c ( T ), F ( x ), and D ( ω ) give helpful interpretations of the exact behavior.